Document Open Access Logo

Who Started This Rumor? Quantifying the Natural Differential Privacy of Gossip Protocols

Authors Aurélien Bellet , Rachid Guerraoui , Hadrien Hendrikx



PDF
Thumbnail PDF

File

LIPIcs.DISC.2020.8.pdf
  • Filesize: 0.63 MB
  • 18 pages

Document Identifiers

Author Details

Aurélien Bellet
  • INRIA, Villeneuve d'Ascq, France
Rachid Guerraoui
  • EPFL, Lausanne, Switzerland
Hadrien Hendrikx
  • PSL, DIENS, INRIA, Paris, France

Cite AsGet BibTex

Aurélien Bellet, Rachid Guerraoui, and Hadrien Hendrikx. Who Started This Rumor? Quantifying the Natural Differential Privacy of Gossip Protocols. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 8:1-8:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DISC.2020.8

Abstract

Gossip protocols (also called rumor spreading or epidemic protocols) are widely used to disseminate information in massive peer-to-peer networks. These protocols are often claimed to guarantee privacy because of the uncertainty they introduce on the node that started the dissemination. But is that claim really true? Can the source of a gossip safely hide in the crowd? This paper examines, for the first time, gossip protocols through a rigorous mathematical framework based on differential privacy to determine the extent to which the source of a gossip can be traceable. Considering the case of a complete graph in which a subset of the nodes are curious, we study a family of gossip protocols parameterized by a "muting" parameter s: nodes stop emitting after each communication with a fixed probability 1-s. We first prove that the standard push protocol, corresponding to the case s = 1, does not satisfy differential privacy for large graphs. In contrast, the protocol with s = 0 (nodes forward only once) achieves optimal privacy guarantees but at the cost of a drastic increase in the spreading time compared to standard push, revealing an interesting tension between privacy and spreading time. Yet, surprisingly, we show that some choices of the muting parameter s lead to protocols that achieve an optimal order of magnitude in both privacy and speed. Privacy guarantees are obtained by showing that only a small fraction of the possible observations by curious nodes have different probabilities when two different nodes start the gossip, since the source node rapidly stops emitting when s is small. The speed is established by analyzing the mean dynamics of the protocol, and leveraging concentration inequalities to bound the deviations from this mean behavior. We also confirm empirically that, with appropriate choices of s, we indeed obtain protocols that are very robust against concrete source location attacks (such as maximum a posteriori estimates) while spreading the information almost as fast as the standard (and non-private) push protocol.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
Keywords
  • Gossip Protocol
  • Rumor Spreading
  • Differential Privacy

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Martín Abadi, Andy Chu, Ian J. Goodfellow, H. Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. In CCS, 2016. Google Scholar
  2. Huseyin Acan, Andrea Collevecchio, Abbas Mehrabian, and Nick Wormald. On the push&pull protocol for rumor spreading. SIAM Journal on Discrete Mathematics, 31(2):647-668, 2017. Google Scholar
  3. Dan Alistarh, Seth Gilbert, Rachid Guerraoui, and Morteza Zadimoghaddam. How efficient can gossip be?(on the cost of resilient information exchange). In ICALP, 2010. Google Scholar
  4. Dana Angluin, James Aspnes, and David Eisenstat. Fast computation by population protocols with a leader. Distributed Computing, 21(3):183-199, 2008. Google Scholar
  5. Borja Balle, James Bell, Adria Gascon, and Kobbi Nissim. The Privacy Blanket of the Shuffle Model. Technical report, arXiv:1903.02837, 2019. Google Scholar
  6. Aurélien Bellet, Rachid Guerraoui, and Hadrien Hendrikx. Who started this rumor? Quantifying the natural differential privacy guarantees of gossip protocols. arXiv preprint arXiv:1902.07138, 2019. Google Scholar
  7. Aurélien Bellet, Rachid Guerraoui, Mahsa Taziki, and Marc Tommasi. Personalized and Private Peer-to-Peer Machine Learning. In AISTATS, 2018. Google Scholar
  8. Petra Berenbrink, Jurek Czyzowicz, Robert Elsässer, and Leszek Gasieniec. Efficient information exchange in the random phone-call model. Automata, Languages and Programming, 2010. Google Scholar
  9. Stephen Boyd, Arpita Ghosh, Balaji Prabhakar, and Devavrat Shah. Randomized gossip algorithms. IEEE Transactions on Information Theory, 52(6):2508-2530, 2006. Google Scholar
  10. Kamalika Chaudhuri, Claire Monteleoni, and Anand D. Sarwate. Differentially Private Empirical Risk Minimization. Journal of Machine Learning Research, 12:1069-1109, 2011. Google Scholar
  11. Albert Cheu, Adam D. Smith, Jonathan Ullman, David Zeber, and Maxim Zhilyaev. Distributed Differential Privacy via Shuffling. Technical report, arXiv:1808.01394, 2018. Google Scholar
  12. Igor Colin, Aurélien Bellet, Joseph Salmon, and Stéphan Clémençon. Gossip dual averaging for decentralized optimization of pairwise functions. In ICML, 2016. Google Scholar
  13. Alan Demers, Dan Greene, Carl Hauser, Wes Irish, John Larson, Scott Shenker, Howard Sturgis, Dan Swinehart, and Doug Terry. Epidemic algorithms for replicated database maintenance. In PODC, 1987. Google Scholar
  14. Benjamin Doerr, Mahmoud Fouz, and Tobias Friedrich. Social networks spread rumors in sublogarithmic time. In STOC, 2011. Google Scholar
  15. John C. Duchi, Alekh Agarwal, and Martin J. Wainwright. Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling. IEEE Transactions on Automatic Control, 57(3):592-606, 2012. Google Scholar
  16. Cynthia Dwork. Differential Privacy. In ICALP, 2006. Google Scholar
  17. Cynthia Dwork, Krishnaram Kenthapadi, Frank McSherry, Ilya Mironov, and Moni Naor. Our data, ourselves: Privacy via distributed noise generation. In EUROCRYPT, 2006. Google Scholar
  18. Cynthia Dwork and Aaron Roth. The algorithmic foundations of differential privacy. Foundations and Trends in Theoretical Computer Science, 9(3-4):211-407, 2014. Google Scholar
  19. Paul Erdős and Alfred Rényi. On a classical problem of probability theory. Publ. Math. Inst. Hung. Acad. Sci., 1961. Google Scholar
  20. Úlfar Erlingsson, Vitaly Feldman, Ilya Mironov, and Ananth Raghunathan abd Kunal Talwar. Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity. Technical report, arXiv:1811.12469, 2018. Google Scholar
  21. Patrick T Eugster, Rachid Guerraoui, Anne-Marie Kermarrec, and Laurent Massoulié. Epidemic information dissemination in distributed systems. Computer, 37(5):60-67, 2004. Google Scholar
  22. Giulia Fanti, Peter Kairouz, Sewoong Oh, Kannan Ramchandran, and Pramod Viswanath. Hiding the rumor source. IEEE Transactions on Information Theory, 2017. Google Scholar
  23. Alan M Frieze and Geoffrey R Grimmett. The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics, 10(1):57-77, 1985. Google Scholar
  24. Chryssis Georgiou, Seth Gilbert, Rachid Guerraoui, and Dariusz R Kowalski. Asynchronous gossip. Journal of the ACM, 60(2):11, 2013. Google Scholar
  25. Chryssis Georgiou, Seth Gilbert, and Dariusz R Kowalski. Confidential gossip. In ICDCS, 2011. Google Scholar
  26. Mohsen Ghaffari and Calvin Newport. How to discreetly spread a rumor in a crowd. In DISC, 2016. Google Scholar
  27. George Giakkoupis, Rachid Guerraoui, Arnaud Jégou, Anne-Marie Kermarrec, and Nupur Mittal. Privacy-conscious information diffusion in social networks. In International Symposium on Distributed Computing, pages 480-496. Springer, 2015. Google Scholar
  28. Karol Gotfryd, Marek Klonowski, and Dominik Pajak. On location hiding in distributed systems. In International Colloquium on Structural Information and Communication Complexity, pages 174-192. Springer, 2017. Google Scholar
  29. Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599-653, 2000. Google Scholar
  30. Zhiyi Huang and Jinyan Liu. Optimal differentially private algorithms for k-means clustering. In PODS, 2018. Google Scholar
  31. Jiaojiao Jiang, Sheng Wen, Shui Yu, Yang Xiang, and Wanlei Zhou. Identifying propagation sources in networks: State-of-the-art and comparative studies. IEEE Communications Surveys & Tutorials, 19(1):465-481, 2017. Google Scholar
  32. Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Keith Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D'Oliveira, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett, Adrià Gascón, Badih Ghazi, Phillip B. Gibbons, Marco Gruteser, Zaid Harchaoui, Chaoyang He, Lie He, Zhouyuan Huo, Ben Hutchinson, Justin Hsu, Martin Jaggi, Tara Javidi, Gauri Joshi, Mikhail Khodak, Jakub Konečný, Aleksandra Korolova, Farinaz Koushanfar, Sanmi Koyejo, Tancrède Lepoint, Yang Liu, Prateek Mittal, Mehryar Mohri, Richard Nock, Ayfer Özgür, Rasmus Pagh, Mariana Raykova, Hang Qi, Daniel Ramage, Ramesh Raskar, Dawn Song, Weikang Song, Sebastian U. Stich, Ziteng Sun, Ananda Theertha Suresh, Florian Tramèr, Praneeth Vepakomma, Jianyu Wang, Li Xiong, Zheng Xu, Qiang Yang, Felix X. Yu, Han Yu, and Sen Zhao. Advances and Open Problems in Federated Learning. Technical report, arXiv:1912.04977, 2019. Google Scholar
  33. Richard Karp, Christian Schindelhauer, Scott Shenker, and Berthold Vocking. Randomized rumor spreading. In FOCS, 2000. Google Scholar
  34. David Kempe, Alin Dobra, and Johannes Gehrke. Gossip-Based Computation of Aggregate Information. In FOCS, 2003. Google Scholar
  35. Anastasia Koloskova, Sebastian Stich, and Martin Jaggi. Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication. In ICML, 2019. Google Scholar
  36. Dariusz R Kowalski and Christopher Thraves Caro. Estimating time complexity of rumor spreading in ad-hoc networks. In International Conference on Ad-Hoc Networks and Wireless, pages 245-256. Springer, 2013. Google Scholar
  37. Wentian Lu and Gerome Miklau. Exponential random graph estimation under differential privacy. In KDD, 2014. Google Scholar
  38. Pedro C Pinto, Patrick Thiran, and Martin Vetterli. Locating the source of diffusion in large-scale networks. Physical Review Letters, 2012. Google Scholar
  39. Boris Pittel. On spreading a rumor. SIAM Journal on Applied Mathematics, 47(1):213-223, 1987. Google Scholar
  40. Sujay Sanghavi, Bruce Hajek, and Laurent Massoulié. Gossiping with multiple messages. IEEE Transactions on Information Theory, 53(12):4640-4654, 2007. Google Scholar
  41. Devavrat Shah and Tauhid Zaman. Rumors in a network: Who’s the culprit? IEEE Transactions on Information Theory, 2011. Google Scholar
  42. Haipei Sun, Xiaokui Xiao, Issa Khalil, Yin Yang, Zhan Qin, Hui Wang, and Ting Yu. Analyzing subgraph statistics from extended local views with decentralized differential privacy. In CCS, 2019. Google Scholar
  43. Paul Vanhaesebrouck, Aurélien Bellet, and Marc Tommasi. Decentralized collaborative learning of personalized models over networks. In AISTATS, 2017. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail